Balmer Rydberg Equation Calculator

To calculate the wavelength (λ) using the Balmer-Rydberg equation, you subtract the inverse square of 2 from the inverse square of the given value of n, multiply by the Rydberg constant (R), and then take the inverse of the product.

Balmer Rydberg Equation Calculator

Enter any 1 value to calculate the missing variable

Principal Quantum Number (n) Wavelength

The Balmer-Rydberg Equation Calculator is used to calculate the wavelength of light that is emitted during electron transitions in a hydrogen atom. This equation is particularly useful in spectroscopy because it can discover the wavelengths in the Balmer series, where electrons drop from a higher energy level to the second energy level (n=2). The Rydberg constant (R) is a fundamental constant used in atomic physics, and the formula helps calculate the wavelength of light emitted when an electron moves between energy levels.

Formula:

Contents

1 Formula:
2 Solved Calculation:
3 What is Balmer Rydberg Equation Calculator?
4 Final Words:

 $\lambda = \frac{1}{R \times \left( \frac{1}{2^2} - \frac{1}{n^2} \right)}$

Variable	Description
λ	Wavelength of light emitted (in meters)
R	Rydberg constant = $1.097 \times 10^7 \, \text{m}^{-1}$
n	Principal quantum number of the energy level (n > 2)

Solved Calculation:

Example 1:

Step	Calculation
Rydberg Constant (R)	$1.097 \times 10^7 \, \text{m}^{-1}$
n (Principal Quantum Number)	3
Wavelength Calculation	$\lambda = \frac{1}{1.097 \times 10^7 \times \left( \frac{1}{4} - \frac{1}{9} \right)}$
Result	$\lambda = 656.3 \, \text{nm}$

Answer: The wavelength for $n = 3$ is 656.3 nm.

Example 2:

Step	Calculation
Rydberg Constant (R)	$1.097 \times 10^7 \, \text{m}^{-1}$
n (Principal Quantum Number)	4
Wavelength Calculation	$\lambda = \frac{1}{1.097 \times 10^7 \times \left( \frac{1}{4} - \frac{1}{16} \right)}$
Result	$\lambda = 486.1 \, \text{nm}$

Answer: The wavelength for $n = 4$ is 486.1 nm.

What is Balmer Rydberg Equation Calculator?

The Balmer Rydberg Equation Calculator is a tool that is used to calculate the wavelengths of light being emitted by electrons as they transition between energy levels in a hydrogen atom. The Balmer-Rydberg equation specifically deals with visible light which is emitted when an electron falls to the second energy level (n=2) from higher levels. The formula is:

Final Words:

Most importantly, the Rydberg constant is a critical part of the calculation, and calculators can help solve for wavelengths or energy level differences in the hydrogen atom using the Balmer formula.